56 lines
4.8 KiB
TeX
56 lines
4.8 KiB
TeX
\section{Related Work}
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\label{sec:relatedWork}
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% 1/2 - 3/4 Seite ca.
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%klassisch resampling
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A common way to handle degeneracy and impoverishment is to apply suitable resampling methods.
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The four most popular and well established approaches found in literature are multinomial-, stratified-, systematic- and residual resampling.
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They are also referred to as traditional methods, since a single distribution is used for resampling and the number of times a particle is re-drawn is always proportional to is weight \cite{Li2015b}.
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%advanced resampling
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A more advanced method, with an adaptive number of particles instead of a fixed one, is KLD-resampling.
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It determines the number of particles to resample so that the Kullback-Leibler divergence between the distribution before resampling and after resampling does not exceed a pre-specified value \cite{Sun2013}.
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The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
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The problem of sample degeneracy and impoverishment is therefore encountered by adapting the number of particles depend upon the systems current uncertainty.
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In \cite{Li2015b} an overview of different resampling approaches are given.
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%allgemien auf andere methoden überleiten
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As seen in the example of KLD-resampling, some resampling methods are able to reduce impoverishment to a certain degree by themselves.
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However, in practice, sample impoverishment is also a problem of environmental restrictions and system dynamics.
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Here, classical resampling schemes fail, since they are not able to propagate new particles into the state space.
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More promising and intelligent solutions are given by techniques of Particle Distribution Optimization (PDO).
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These variations of techniques are acting in different ways to optimize the spatial distribution of particles and are particularly effective in alleviating sample degeneracy and impoverishment \cite{Li2014}.
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For example in \cite{Xiaoqin2008} a Particle Swarm Optimization is used as importance distribution for visual tracking.
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Particles are iteratively updated according to their own experience and the experience of the swarm (or neighboring particles).
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This allows for a multi-layer importance sampling and incorporation of the current measurements into the importance distribution, dealing with the sample impoverishment.
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Other PDO methods are presented in \cite{Li2014}.
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%hinführen zu IMM
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In context of this work, our aim is to present a general solution that can easily be adapted to common localisation systems.
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A promising approach for an easy to deploy PDO are Interacting Multiple Models (IMM) \cite{Bar-Shalom1988}.
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IMMs are able to mix appropriate systems based on a Bayesian probability metric and Gaussian noise.
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Therefore, a set of modes, like Kalman filters, are running in parallel.
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The mixing between modes is done by using a Markov Chain process, providing a probability for every mode and a transition matrix for switching between them.
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The most proper mode is then chosen for the current state estimation, what allows
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the right choice for every instant in time.
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For example, \cite{Zhang2013} deploys an IMM for a time difference of arrival (TDOA) based localisation using an ultrasonic system.
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Here, line-of-sight (LOS) and non-line-of-sight (NLOS) measurement noises are considered through switching between two extended Kalman filters, one for each condition.
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Thereby, they are able to provide a robust and stable position estimation with high accuracy in both LOS and NLOS noise scenarios.
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An extension to particle filters, and therefore to non-linear and non-Gaussian system, was presented by \cite{Boers2003}.
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The so called Interacting Multiple Model Particle Filter (IMMPF) was then further developed by \cite{Driessen2005}, adding a direct sampling approach.
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This allows a merging between different particle filters by providing a possibility for each filter to sample additional particles from all available particle sets and not just from its own.
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It is obvious that the possibility to draw from other particle sets is based on the mode's probability and the transition matrix provided by the Markov Chain process and therefore does not violate the Markov property.
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Now, the key idea of this work is to satisfy the trade-off between diversity and focus by using appropriate modes within the IMMPF.
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Warum? Weil die meinsten loca systeme auf particle filtern basieren und deswegen bietet es sich an. es erlaubt bereits vorhandene methoden die auf die jeweils einzeln auf die probleme eingehen zu kombinieren und so ein hybrid zu schaffen.
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%Therefore, two different dynamical models are utilized and a novel approach for a non-trivial Markov switching Process based on Kullback-Leibler divergence and a Wi-Fi quality factor are presented.
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